The order of the remainder in derivatives of composition and inverse operators for \(p\)-variation norms

DOI10.1214/aos/1176325354zbMath0816.62039OpenAlexW4250476802MaRDI QIDQ1327829

Richard M. Dudley

Publication date: 3 July 1995

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176325354

zbMATH Keywords

inverse operatorcomposition operatorcompact setsempirical distribution functionsFrechet differentiabilityHadamard derivativecompact differentiabilityGateaux derivativesup norm\(p\)-variation normsBahadur-Kiefer theoremsOrlicz variationremainder bounds

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Functional limit theorems; invariance principles (60F17) Applications of functional analysis in probability theory and statistics (46N30) Derivatives of functions in infinite-dimensional spaces (46G05) Functions of bounded variation, generalizations (26A45) Nonparametric inference (62G99)

Related Items (9)

Speed of convergence of classical empirical processes in \(p\)-variation norm ⋮ The index theorem of topological regular variation and its applications ⋮ A study of a class of weighted bootstrap for censored data ⋮ Essential properties of \(L_{p,q}\) spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time ⋮ Rough functions: \(p\)-variation, calculus, and index estimation ⋮ On Bernstein approximants and the \(\varphi\)-variation of a fuzzy random variable ⋮ The Bahadur-Kiefer representation for \(U\)-quantiles ⋮ The operator of inversion as an everywhere continuous nowhere differentiable function ⋮ The \(p\)-variation of partial sum processes and the empirical process

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